I wrote a series on handwriting, and imron suggested I make it a thread, as more people look at threads, but I kind of like how all the content is organized in a blog, so I'm starting this thread and linking to the blog.
I considered writing a bit about technique/motor skills but I decided that was outside the scope of "the minimum requirements" and gets too subjective. It leaves the realm of science and steps into the bounds of art. And by "art" I mean both a refined skill and something that has to do with aesthetics. Of course I have some strong preferences regarding certain aesthetic properties, but these things don't make the difference between a right and wrong character. And so, I just decided to end this series on "the minimum requirements" with some extra practice in the form of a quiz, and leave discussion of other stuff to a thread maybe.
So, regarding technique. I hope you have looked into ergonomic pen grips. All else being equal, right-handed people will have an easier time writing Chinese. High pressure stroke endings are always on the right. Horizontal strokes are slanted up on the right. This comes not from aesthetics but biology. Anyway, assuming right-handedness the generally recommended grip is to have the back of the stick resting on the web between your index finger and thumb, while holding the front in three points with your thumb tip, index finger tip, and side of your middle finger, not necessarily equidistant to the tip.
About writing instruments. You should notice that although my examples were written with a pencil, there was some line width variation. As you can imagine, this is achieved by varying pressure, as paper is soft. The effect is easier to achieve if the paper is on a soft surface, such as more paper. A ballpoint pen can also achieve a similar effect. As for fountain pens, I often read recommendations for them and I might be guilty of recommending them in the past. Although they do require much less pressure than most writing instruments, line width variation is difficult to achieve with them. The thickness is always about the width of the nib. This is OK when writing a language that uses Latin characters, but for Chinese, when in regular script (楷書) one might desire some variation and in cursive (行書) or supercursive (草書, I'm not satisfied with current translations of this term) variation is required, else essential and nonessential strokes are not differentiated. Chinese is easiest to write with a brush. It requires even less pressure than a fountain pen and benefits from having an axis of rotation high up off the plane of the paper. If only they were not so fragile and fussy, a brush would still be the most common writing instrument for Chinese.
Another thing. All else being equal, vertical orthography looks better. In regular script and cursive, "horizontal" strokes slant up at the right, while vertical strokes are mostly truly vertical. In horizontal orthography, the "horizontal" strokes form imaginary lines that stagger against each other from character to character. In vertical orthography, the vertical lines follow text direction, so there is no such effect. And of course, supercursive must be written vertically. Doing otherwise would be like attempting to write English in cursive vertically.
About grids. In the series you can see by my haphazard alignment that I pretty much ignored the grids. However, they can help you align things and judge distances if you care to use them. Different types will help with different things. For casual writing I prefer a single vertical dashed line, marking the center of the line of text, and no boundaries between characters, allowing me to make them as tall or short as I want.